Magnetoplasmonics beyond Metals: Ultrahigh Sensing Performance in Transparent Conductive Oxide Nanocrystals

Active modulation of the plasmonic response is at the forefront of today’s research in nano-optics. For a fast and reversible modulation, external magnetic fields are among the most promising approaches. However, fundamental limitations of metals hamper the applicability of magnetoplasmonics in real-life active devices. While improved magnetic modulation is achievable using ferromagnetic or ferromagnetic-noble metal hybrid nanostructures, these suffer from severely broadened plasmonic response, ultimately decreasing their performance. Here we propose a paradigm shift in the choice of materials, demonstrating for the first time the outstanding magnetoplasmonic performance of transparent conductive oxide nanocrystals with plasmon resonance in the near-infrared. We report the highest magneto-optical response for a nonmagnetic plasmonic material employing F- and In-codoped CdO nanocrystals, due to the low carrier effective mass and the reduced plasmon line width. The performance of state-of-the-art ferromagnetic nanostructures in magnetoplasmonic refractometric sensing experiments are exceeded, challenging current best-in-class localized plasmon-based approaches.

chopper. A third lock-in amplifier locked to the chopper is used to retrieve the total light collected by the detector. The MO signal is calibrated using a K3Fe(CN)6 solution as a standard reference sample, 72 in order to calibrate the ratio between the AC and the DC signal that reaches the detector.
A Hall probe is employed to measure the effective magnetic field in the sample position. The spurious dichroic signal of the set up was subtracted by measuring the MO signals at +1.4 Tesla and -1.4 Tesla: the semi-difference between the two gives the MO signal, assuming that the natural dichroism and optical rotation are invariant with the magnetic field. The measurements were performed in solution, using 1 mm quartz QX cuvettes. The Faraday rotation and ellipticity of the solvent were collected in the same experimental conditions and subtracted from the signal of the sample, in order to isolate the contribution of the NCs. The MO signal was then normalized for the optical density and for the applied magnetic field, and converted into ellipticity and rotation angles (in degrees) according to previous work. 64,66 The optical density of the NC dispersions analysed was in the range 0.7-1.4, which is in the optimal range that maximizes the signal-to-noise ratio. 64 The MO spectra reported in the main text are collected at 1.4 Tesla, and normalized for the optical density and the applied magnetic field.
Analytical Calculation of the optical and magneto-optical response. The calculation of the optical and magneto-optical response was performed with an analytical model previously developed. 27,63 The Drude dielectric function of the semiconductors was inserted in the quasi-static field-and helicity-dependent polarizability (equation S 4). The fitting of extinction and ellipticity spectra was performed using the same analytical model, extracting carrier parameters N, m and . More details are provided in section S2.

S3. Analitical model and fitting of extinction and magneto-optical spectra
To fit the normalized extinction, Faraday ellipticity and rotation spectra, a matlab routine was developed, according to an analytical model introduced in previous work. 1,2 In the dipolar quasi-static approximation, the polarizability of a spherical NC of size D and dielectric where e and m are the charge and effective mass of the electron, v its velocity,  is the damping parameter and B is the external magnetic induction. Commonly, the effect of the magnetic field on the dielectric function of a metal is treated adding an off-diagonal term in the dielectric tensor or in the polarizability tensor, which takes into account for the magnetic-field driven modification of the dielectric function. 4,6 Alternatively, the problem can be also solved by using a diagonal form of the polarizability, as reported by Gu where the second term at the numerator and denominator describes the effect of the magnetic field on the polarizability, in which ( ) = 1 + 2 and are the coupling functions describing the interaction with the magnetic field for the NC and the medium. At zero applied magnetic field, Equation S 4 is simplified to the well-known quasi-static polarizability of a sphere (Equation S 1).
Considering the symmetry of the problem, a change in helicity is equivalent to an inversion of the direction of the external magnetic field B. It follows that the differential polarizability (ΔαB(ω) = αLCP(ω) -αRCP(ω)) can be obtained from the difference between the polarizability calculated with positive and negative applied field. Using the obtained , the helicity-dependent normalized differential cross section can be readily obtained through Equation S 5.
The  can be converted from differential absorption units into ellipticity angle (F) using Equation S 7. The following equations were thus employed to fit the normalized extinction and Faraday ellipticity spectra: Indeed, dopant impurities are known to give rise to electron-scattering which is generally rationalized with the presence of two damping regimes: one at high frequency, characterized by a damping constant , where the electrons can escape the Coulomb interaction with the impurity ions, as they travel faster; and one at low frequency, characterized by , where the damping is higher. 9,10 The two regimes are separated by a frequency threshold , while the width of the crossing region between the two regimes is expressed by .
The different behaviour between ITO and FICO can be explained with the fact that Sn 4+ ions scatter electrons more efficiently than In 3+ , 11 due to the higher charge. In addition, the electron scattering is negligible for the Fco-dopant in FICO, due to its lower charge with respect to the Sn 4+ and In 3+ impurities. 12 Alternative fitting approaches reported in the literature reproduced with good agreement the asymmetric line shape of the LSPR in ITO NCs by considering a distribution of carrier densities. 7 Employing the latter model similar agreement with the experimental extinction and MCD was obtained (not reported here), as well as comparable free carrier parameters.
Parameters obtained from the fitting are reported in Table S1, while the  (), used for ITO is reported in Figure S 2C and Table S 2. The fitting curves obtained with this approach, employed on the three experimental spectra, are the one reported in Figure 3 of the main text.
Alternatively, one can fit simultaneously only extinction and ellipticity spectra ( Figure S2 for ITO and Figure S3 for FICO NCs), obtaining similar agreement with the experimental curves, as well as retrieving comparable free electron parameters. In some cases this latter double simultaneous fit (Extinction and Faraday ellipticity) may be preferrable as the measurement of Faraday rotation can be challenging especially for the subtraction of the solvent contribution.

S4. Sensing experiments
The refractive index of the solvents used in the main text were taken from the literature. 13,14 As can be seen in Figure S5, the dispersion curve is quite flat in the region of interest (1200-2400 nm) for all the three solvents, which makes reasonable for us to take a constant value for the refractive index of the solvent.